Dynamics of non-Abelian strings in the theory interpolating from N=2 to N=1 supersymmetric QCD

Physical Review D - Particles, Fields, Gravitation and Cosmology. 2020. Vol. 101. No. 1. Article 014013.

Gorsky A., E. Ievlev, A. Yung

We study the dynamics of non-Abelian vortex strings supported in N =2 supersymmetric QCD with
the U(N) gauge group and N_f = N quark flavors deformed by the mass μ of the adjoint matter. In the limit
of large μ the bulk four-dimensional theory flows to N = 1 supersymmetric QCD. The dynamics of
orientational zero modes of the non-Abelian string is described by the world sheet CP(N − 1) model. At
μ = 0 this model has N =(2, 2) supersymmetry while at large μ it flows to the nonsupersymmetric
CP(N − 1) model. We solve the world sheet model in the large N approximation and find a rich phase
structure with respect to the deformation parameter μ and quark mass differences. The phases include two
strong coupling phases and two Higgs phases. In particular, the Higgs phase at small μ supports CP(N − 1) model kinks representing confined monopoles of the bulk QCD, while in the large-μ Higgs phase
monopoles disappear.

Keywords: quantum field theory, supersymmetry, Sigma Models